Stochastic models of tumour development and related mesoscopic equations

Abstract

We consider different mathematical models inspired by the problems of medicine, in particular, the tumour growth and the related topics. We demonstrate how to starting from an individual-based (microscopic) description, which characterizes cells' behaviour, derive the socalled kinetic (mesoscopic) equations, which describe the approximate system density. Properties of the solutions to the mesoscopic equations (in particular, their long-time behaviour) reflect statistical characteristics of the whole system and demonstrate the corresponding dependence on the system parameters.